Tuning the Atoms 249
one of the motions within the molecules of hydrogen. ” He notes that many other possible
“ overtones ” of this fundamental vibration should be found in the spectrum, though they
had not observed heretofore, for “ if the law of this undulation were the same as that of
the motion of a point near the end of a violin-string, and of a periodic time sufficiently
long (as, for example, two million-millionths of a second), this undulation, when analyzed
by the prism, would give a spectrum covered with lines ruled at intervals about the same
as that between the two [sodium] D lines. ”^10 By considering the atom as essentially analo-
gous to a violin string, Stoney could “ hear ” its spectra as comprising the full complement
of its “ overtones, ” thus also predicting the positions of spectral lines still unobserved.
Stoney continued to pursue the implications of his violin-string model, but he unfortu-
nately left aside the case of hydrogen, seemingly forgetting to include the other visible
line, H γ ; instead he and a collaborator went on to try their luck with a much more complex
molecule (chlorochromic anhydride, CrO 2 Cl 2 ), which gave a much more simple, regular
spectrum than hydrogen ( figure 16.3 ).^11 Though they were successful in applying
the violin-string model in this case, Stoney left suspended the full relation between the
musical model and the observed hydrogen lines; in 1880 he noted that the missing H γ
could be understood as a thirty-fifth harmonic of the same fundamental tone as the other
hydrogen lines, but did not go further to address other possible overtones and their respec-
tive spectral lines.^12
Specifying the structure of the hydrogen “ overtones ” was achieved by Johann Balmer,
a Swiss mathematician who taught at a school for girls in Basel and who was sixty years
old in 1885 when he published his account of the hydrogen spectral lines, his first paper
on physics of any kind. Though he was a geometer, a friend directed him to this problem,
for which Balmer ’ s point of departure was a presentation Helmholtz gave in 1880 at the
Royal Academy of new measurements of the hydrogen spectral lines, including several
newly observed lines in the violet and ultraviolet, which also were prominent in the spectra
of white stars. Balmer emphasizes the importance of “ hydrogen, the atomic weight of
which is by far the smallest of all substances known to date and characterizes it as the
simplest chemical element, that substance through the refraction of analyzed light in solar
spectrum gives us perceptible knowledge of the powerful motions and forces that theFigure 16.3
Stoney and Reynolds ’ s spectrum of chlorochromic anhydride (CrO 2 Cl 2 ), showing its evenly spaced lines in the
green-yellow (1871).